Basic substructural core fuzzy logics and their extensions: Mianorm-based logics

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• 作者：Eunsuk Yang ; ^{eunsyang@jbnu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Substructural logics ; MIA operators ; Mianorms ; Non-associative ; non-commutative fuzzy logics
• 刊名：Fuzzy Sets and Systems
• 出版年：2016
• 出版时间：15 October 2016
• 年：2016
• 卷：301
• 期：Complete
• 页码：1-18
• 全文大小：390 K

文摘

This paper addresses standard completeness for non-associative, non-commutative, substructural fuzzy logics and their axiomatic extensions. First, fuzzy systems, which are based on mianorms   (binary monotonic identity aggregation operations on the real unit interval [0,1]$[0,1]$), their corresponding algebraic structures, and algebraic completeness results are discussed. Next, completeness with respect to algebras whose lattice reduct is [0,1]$[0,1]$, so-called standard completeness, is established for these systems using construction in the style of Jenei–Montagna. Finally, some axiomatic extensions of the non-associative, non-commutative core fuzzy logics having axioms corresponding to the structural rule(s) of exchange and/or associativity are considered.